When \(h=0\) , () reduces to Bregman PDHG [1]}.
When \(g=0\) , \(g^\ast = \delta _{\lbrace 0\rbrace }\)  (and assuming \(z^{(0)}=0\) ),
we obtain the Bregman proximal gradient algorithm [2]}.
When \(f=0\)  in (), we obtain the
Bregman Loris–Verhoeven algorithm with shift:
\(x^{(k+1)} &= \mathop {\rm argmin}_x {\big (\langle \nabla h(x^{(k)})-A^Tz^{(k)}, x\rangle +\frac{1}{\tau }d_\mathrm {p}(x,x^{(k)})\big )} \\z^{(k+1)} &= \mathrm {prox}^{\phi _\mathrm {d}}_{\sigma g^\ast } \big (z^{(k)},-\sigma A(2x^{(k+1)}-x^{(k)}) \big ).\) 
